Doc5 - 2. Find the unique solution for each of the...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2. Find the unique solution for each of the following recur- rence relations. a} on“ — 1.5::n = fl, rt 30 lad-41.1,, — 5d,,_. = l3, rt 3] e] 3a,,“ #441,, =0, nail, n; =5 (1} En” —3o,,_. =0, :23 i, :14 =3] 4. The number of bacteria in a culture is 1000 {approximately}, and this number increases 259% ever},f two hours. Use a recur- rence relation to determine the number of bacteria present after one day. 10. Fora 2: Lapermutation pl, p2, p3. , , . , p" oftheintegers, 2, 3, . , , , n is called orderly if, for each i = l, 2, 3, . . ., n — Lthere esistsaj o» isUchthatIpJ. — p,| = i.[lf.n = 2,1]1e permutations 1, land 2, l are both orderly. Whenn = 3we find that 3, l, 2 is an orderly permutation, while 2, 3, 1 is not. [‘d‘r‘h}r not?)] [a] List all the orllzlerlg,r permutations for i, 2, 3. {In} List all the orderly permutations for l, 2. 3, 4. {c} If p], p2, p3, p4, p5 is an orderlyr permutation of l, 2, 3, 4, 5, what value[s] can pl be? {d} For rt :- 1, let an count the number of orderlyr permu- tations for l, 2, 3, .. . , n. Find and solve a recurrence relation for on. 16. For n 3 i. let on be the number of ways to write a as an or- dered sum of positive integers, where each summand is at least 2. (For example. :15 = 3 becaUse here we may represent 5 by 5, by 2 + 3, and by 3 + 2.) Find and solve a remrrence relation for an. 24. Porn 3 l, let can count the number of ways to tile 3 2 X n chessboard using horizontal (1 X 2] dominoes [which can also be used as vertical (2 X l] dominoes] and square [2 X 2) tiles. Find and solve a recurrence relation for a". 26. Let}: = {f}. l} andrt = [[1, [i], ii} g E*.Forn 31,]etnn count the number of shings in A“ of length it. Find and solve a recurrence relation for on . 10. The general solution of the recurrence relation a”: + blots“ +b2an = bgn + .54, n 30, with b. constant for l 5 i 5 4, is (3.2” +1323" +n — 7. Find .6, for each I fit 54. 12. Let E = {[1, L 2, 3}. Fern 3 Lletnr,1 count the number of strings in E" containing an odd number of 1’s. Find and solve a recurrence relation for an. ...
View Full Document

This note was uploaded on 10/01/2011 for the course MACM 101 taught by Professor Pearce during the Spring '08 term at Simon Fraser.

Page1 / 3

Doc5 - 2. Find the unique solution for each of the...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online